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Difference between revisions of "Isolated point"

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''of a subspace <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/i/i052/i052770/i0527701.png" /> of a topological space <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/i/i052/i052770/i0527702.png" />''
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''of a subspace $A$ of a topological space $X$''
  
A point <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/i/i052/i052770/i0527703.png" /> such that the intersection of some [[Neighbourhood|neighbourhood]] of it with <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/i/i052/i052770/i0527704.png" /> consists of the point <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/i/i052/i052770/i0527705.png" /> alone.
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A point $a\in A$ such that the intersection of some [[Neighbourhood|neighbourhood]] of it with $A$ consists of the point $a$ alone.

Revision as of 17:16, 11 April 2014

of a subspace $A$ of a topological space $X$

A point $a\in A$ such that the intersection of some neighbourhood of it with $A$ consists of the point $a$ alone.

How to Cite This Entry:
Isolated point. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Isolated_point&oldid=31527
This article was adapted from an original article by A.A. Mal'tsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article